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Nonlinear Schrödinger equations with strongly singular potentials

Bellazzini, Jacopo and Bonanno, Claudio (2010) Nonlinear Schrödinger equations with strongly singular potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 140 (4), p. 707-721. eISSN 1473-7124. Article.

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DOI: 10.1017/S0308210509001401

Abstract

We look for standing waves for nonlinear Schrödinger equations
i ∂ψ/∂t +Δψ − g(|y|)ψ −W' (|ψ|) ψ /|ψ| = 0
with cylindrically symmetric potentials g vanishing at infinity and non-increasing, and a C1 nonlinear term satisfying weak assumptions. In particular, we show the existence of standing waves with non-vanishing angular momentum with prescribed L2 norm. The solutions are obtained via a minimization argument, and the proof is given for an abstract functional which presents a lack of compactness. As a specific case, we prove the existence of standing waves with non-vanishing angular momentum for the nonlinear hydrogen atom equation.

Item Type:Article
ID Code:6930
Status:Published
Refereed:Yes
Uncontrolled Keywords:Nonlinear Schroedinger (NLS) equations, eigenvalue problem, elliptic equations
Divisions:001 Università di Sassari > 01 Dipartimenti > Scienze botaniche, ecologiche e geologiche
Publisher:Cambridge University Press
eISSN:1473-7124
Copyright Holders:© 2010 The Royal Society of Edinburgh
Deposited On:10 Jan 2012 13:14

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